This invention relates to process control and, more particularly, to improved apparatus and methods for statistical control of processes.
Process control is a method for controlling the operational parameters of a process by monitoring one or more of its characteristics over time. It is used to ensure that the quality and efficiency of the process do not vary substantially during a single run or over the course of several runs. While process control is typically employed in the manufacturing industry, it also has application in the service industry.
One form of process control, statistical process control (SPC), relies on statistical analysis of process variables to ensure that the process is operating in a desired manner. SPC is based on the assumption that there is a random variation in the values of each variable (e.g., tensile strength, degree of brightness, etc.) that serves as a measure of process quality or efficiency. If those variables consistently exhibit a normal distribution pattern (e.g., Gaussian) within established limits, then the process is in statistical control. Variation from this normal distribution indicates that the process is not in statistical control.
For example, brightness may be an indicator of the quality of paper produced by a particular manufacturing process. To ensure that the process is in control, brightness values are measured at discrete intervals during a run, i.e., during operation of the process. By plotting those values and comparing them with a desired target brightness level, it is possible to detect undesirable shifts in the process. Once alerted, the operator can take compensating steps, such as increasing or conversely reducing the amount of bleaching agent added to the batch.
Among the prior art SPC methods is the cumulative sum (CUSUM) procedure. This employs a form of a sequential likelihood ratio test that evaluates the hypothesis that the mean of a process is equal to a target value against the alternative hypothesis that the mean deviates from that value by a specified amount.
As described for example by Ulery, "Software requirements for Statistical Quality Control," Instrument Society of America Paper #86-2713 (1986), a computational CUSUM procedure tracks two cumulative sums, a high-value sum S.sub.H and a low-value sum S.sub.L, expressed as follows: EQU S.sub.H (i)=max [0, Y.sub.i -k+S.sub.H (i-1)] EQU S.sub.L (i)=max [0,-k-Y.sub.i +A.sub.L (i-1)]
where, Y.sub.i is a standardized variable equal to the observed value sample average minus the target value divided by the standard deviation of the sample average, k is a slack value, and max[. . . ] is a function that returns the value of its numerically largest parameter.
Prior SPC systems using this CUSUM method signal an out-of-control situation when either S.sub.H or S.sub.L exceeds a predetermined alarm value. Typically, an operator responds to the signal by deciding what action, if any, to take with respect to the alarm condition.
While prior CUSUM systems have met at least limited success, they do not permit accurate control of a wide range or variety of processes. Accordingly, an object of this invention is to provide improved apparatus and methods for statistical process control.
A further object of the invention is to provide an improved process control system that statistically interprets measured process variables to identify out-of-control situations and automatically corrects them.